A model for the control of Echinococcus multilocularis in France

Mathematical Global Dynamics and Control Strategies on Echinococcus multilocularis Infection

Echinococcus multilocularis, a major cause of echinococcosis in human, is a parasitic sylvatic disease between two major hosts in a predator-prey relation. A new model for the transmission dynamics of Echinococcus multilocularis in the population of red foxes and voles with environment as a source of infection is formulated and rigorously analyzed. The model is used to access the impact of treatment on red foxes and environmental disinfection as control strategies on the disease dynamics. The control reproduction number is computed and is used to rigorously prove the local and global dynamics of models' equilibria. Using available data on Echinococcus, elasticity indices and partial rank correlation coefficients of control reproduction number and cumulative new cases in red foxes and voles are computed. Parameters that have high influence locally and globally are identified. Numerical experiments indicate that administering disinfection of environment only induces more positive impact than applying treatment only on red foxes in controlling the infection. Generally, interventions towards treating red foxes and environmental disinfection could be sufficient in tackling transmission of disease in the populations.

Strategies for tackling Taenia solium taeniosis/cysticercosis: A systematic review and comparison of transmission models, including an assessment of the wider Taeniidae family transmission models

Background

The cestode Taenia solium causes the neglected (zoonotic) tropical disease cysticercosis, a leading cause of preventable epilepsy in endemic low and middle-income countries. Transmission models can inform current scaling-up of control efforts by helping to identify, validate and optimise control and elimination strategies as proposed by the World Health Organization (WHO).

Methodology/Principal findings

A systematic literature search was conducted using the PRISMA approach to identify and compare existing T. solium transmission models, and related Taeniidae infection transmission models. In total, 28 modelling papers were identified, of which four modelled T. solium exclusively. Different modelling approaches for T. solium included deterministic, Reed-Frost, individual-based, decision-tree, and conceptual frameworks. Simulated interventions across models agreed on the importance of coverage for impactful effectiveness to be achieved.

Other Taeniidae infection transmission models comprised force-of-infection (FoI), population-based (mainly Echinococcus granulosus) and individual-based (mainly E. multilocularis) modelling approaches. Spatial structure has also been incorporated (E. multilocularis and Taenia ovis) in recognition of spatial aggregation of parasite eggs in the environment and movement of wild animal host populations.

Conclusions/Significance

Gaps identified from examining the wider Taeniidae family models highlighted the potential role of FoI modelling to inform model parameterisation, as well as the need for spatial modelling and suitable structuring of interventions as key areas for future T. solium model development. We conclude that working with field partners to address data gaps and conducting cross-model validation with baseline and longitudinal data will be critical to building consensus-led and epidemiological setting-appropriate intervention strategies to help fulfil the WHO targets.

Taenia solium infection in humans (taeniosis and neurocysticercosis) and pigs (cysticercosis) presents a significant global public health and economic challenge. The World Health Organization has called for validated strategies and wider consensus on which strategies are suitable for different epidemiological settings to support successful T. solium control and elimination efforts. Transmission models can be used to inform these strategies. Therefore, a modelling review was undertaken to assess the current state and gaps relating to T. solium epidemiological modelling. The literature surrounding models for other Taeniidae family infections was also considered, identifying approaches to aid further development of existing T. solium models. A variety of different modelling approaches have been used for T. solium including differences in structural and parametric assumptions associated with T. solium transmission biology. Despite these differences, all models agreed on the importance of coverage on intervention effectiveness. Other Taeniidae family models highlighted the need for incorporating spatial structure when necessary to capture aggregation of transmission stages in the environment and movement of animal hosts.

Rabies Vaccination Targets for Stray Dog Populations

The role of stray dogs in the persistence of domestic dog rabies, and whether removal of such dogs is beneficial, remains contentious issues for control programs seeking to eliminate rabies. While a community might reach the WHO vaccination target of 70% for dogs that can be handled, the stray or neighborhood dogs that are too wary of humans to be held are a more problematic population to vaccinate. Here, we present a method to estimate vaccination targets for stray dogs when the dog population is made up of stray, free-roaming, and confined dogs, where the latter two types are considered to have an identifiable owner. The control effort required for stray dogs is determined by the type-reproduction number, T1, the number of stray dogs infected by one rabid stray dog either directly or via any chain of infection involving owned dogs. Like the basic reproduction number R0 for single host populations, T1 determines the vaccination effort required to control the spread of disease when control is targeted at one host type, and there is a mix of host types. The application of T1 to rabies in mixed populations of stray and owned dogs is novel. We show that the outcome is sensitive to the vaccination coverage in the owned dog population, such that if vaccination rates of owned dogs were too low then no control effort targeting stray dogs is able to control or eliminate rabies. The required vaccination level also depends on the composition of the dog population, where a high proportion of either stray or free-roaming dogs implies unrealistically high vaccination levels are required to prevent rabies. We find that the required control effort is less sensitive to continuous culling that increases the death rate of stray dogs than to changes in the carrying capacity of the stray dog population.

Modeling the transmission dynamics and control of rabies in China

Human rabies was first recorded in ancient China in about 556 BC and is still one of the major public-health problems in China. From 1950 to 2015, 130,494 human rabies cases were reported in Mainland China with an average of 1977 cases per year. It is estimated that 95% of these human rabies cases are due to dog bites. The purpose of this article is to provide a review about the models, results, and simulations that we have obtained recently on studying the transmission of rabies in China. We first construct a basic susceptible, exposed, infectious, and recovered (SEIR) type model for the spread of rabies virus among dogs and from dogs to humans and use the model to simulate the human rabies data in China from 1996 to 2010. Then we modify the basic model by including both domestic and stray dogs and apply the model to simulate the human rabies data from Guangdong Province, China. To study the seasonality of rabies, in Section 4 we further propose a SEIR model with periodic transmission rates and employ the model to simulate the monthly data of human rabies cases reported by the Chinese Ministry of Health from January 2004 to December 2010. To understand the spatial spread of rabies, in Section 5 we add diffusion to the dog population in the basic SEIR model to obtain a reaction-diffusion equation model and determine the minimum wave speed connecting the disease-free equilibrium to the endemic equilibrium. Finally, in order to investigate how the movement of dogs affects the geographically inter-provincial spread of rabies in Mainland China, in Section 6 we propose a multi-patch model to describe the transmission dynamics of rabies between dogs and humans and use the two-patch submodel to investigate the rabies virus clades lineages and to simulate the human rabies data from Guizhou and Guangxi, Hebei and Fujian, and Sichuan and Shaanxi, respectively. Some discussions are provided in Section 7.

Dynamics of the force of infection: insights from Echinococcus multilocularis infection in foxes

Characterizing the force of infection (FOI) is an essential part of planning cost effective control strategies for zoonotic diseases. Echinococcus multilocularis is the causative agent of alveolar echinococcosis in humans, a serious disease with a high fatality rate and an increasing global spread. Red foxes are high prevalence hosts of E. multilocularis. Through a mathematical modelling approach, using field data collected from in and around the city of Zurich, Switzerland, we find compelling evidence that the FOI is periodic with highly variable amplitude, and, while this amplitude is similar across habitat types, the mean FOI differs markedly between urban and periurban habitats suggesting a considerable risk differential. The FOI, during an annual cycle, ranges from (0.1,0.8) insults (95% CI) in urban habitat in the summer to (9.4, 9.7) (95% CI) in periurban (rural) habitat in winter. Such large temporal and spatial variations in FOI suggest that control strategies are optimal when tailored to local FOI dynamics.

Human alveolar echinococcosis (AE) is caused by the fox tapeworm E. multilocularis and has a high fatality rate if untreated. The frequency of the tapeworm in foxes can be reduced through the regular distribution of anthelmintic baits and thus decrease the risk of zoonotic transmission. Here, we estimate the force of infection to foxes using a mathematical model and data from necropsied foxes. The results suggest that the frequency of anthelmintic baiting of foxes can be optimised to local variations in transmission that depend upon season and type of fox habitat.

Synthesising 30 years of mathematical modelling of Echinococcus transmission

BACKGROUND

Echinococcosis is a complex zoonosis that has domestic and sylvatic lifecycles, and a range of different intermediate and definitive host species. The complexities of its transmission and the sparse evidence on the effectiveness of control strategies in diverse settings provide significant challenges for the design of effective public health policy against this disease. Mathematical modelling is a useful tool for simulating control packages under locally specific transmission conditions to inform optimal timing and frequency of phased interventions for cost-effective control of echinococcosis. The aims of this review of 30 years of Echinococcus modelling were to discern the epidemiological mechanisms underpinning models of Echinococcus granulosus and E. multilocularis transmission and to establish the need to include a human transmission component in such models.

METHODOLOGY/PRINCIPAL FINDINGS

A search was conducted of all relevant articles published up until July 2012, identified from the PubMED, Web of Knowledge and Medline databases and review of bibliographies of selected papers. Papers eligible for inclusion were those describing the design of a new model, or modification of an existing mathematical model of E. granulosus or E. multilocularis transmission. A total of 13 eligible papers were identified, five of which described mathematical models of E. granulosus and eight that described E. multilocularis transmission. These models varied primarily on the basis of six key mechanisms that all have the capacity to modulate model dynamics, qualitatively affecting projections. These are: 1) the inclusion of a 'latent' class and/or time delay from host exposure to infectiousness; 2) an age structure for animal hosts; 3) the presence of density-dependent constraints; 4) accounting for seasonality; 5) stochastic parameters; and 6) inclusion of spatial and risk structures.

CONCLUSIONS/SIGNIFICANCE

This review discusses the conditions under which these mechanisms may be important for inclusion in models of Echinococcus transmission and proposes recommendations for the design of dynamic human models of transmission. Accounting for the dynamic behaviour of the Echinococcus parasites in humans will be key to predicting changes in the disease burden over time and to simulate control strategies that optimise public health impact.

Efficiency of spatio-temporal vaccination regimes in wildlife populations under different viral constraints

Classical Swine Fever (CSF) is considered an endemic disease in European wild boar populations. In view of the high economic impact of the introduction of the virus into domestic pig units, huge efforts are invested in the preventive control of CSF in wild boar populations. Recent European Community guidelines favour oral mass vaccination against CSF in wild boar populations. The guidelines are explicit on the temporal structure of the vaccination protocol, but little is known about the efficacy of different spatial application schemes, or how they relate to outbreak dynamics.

We use a spatially explicit, individual-based wild boar model that represents the ecology of the hosts and the epidemiology of CSF, both on a regional scale and on the level of individual course of infection. We simulate adaptive spatial vaccination schemes accounting for the acute spread of an outbreak while using the temporal vaccination protocol proposed in the Community guidelines.

Vaccination was found to be beneficial in a wide range of scenarios. We show that the short-term proactive component of a vaccination strategy is not only as decisive as short-term continuity, but also that it can outcompete alternative practices while being practically feasible. Furthermore, we show that under certain virus-host conditions vaccination might actually contribute to disease persistence in local populations.

Analysis of rabies in China: transmission dynamics and control

Human rabies is one of the major public-health problems in China. The number of human rabies cases has increased dramatically in the last 15 years, partially due to the poor understanding of the transmission dynamics of rabies and the lack of effective control measures of the disease. In this article, in order to explore effective control and prevention measures we propose a deterministic model to study the transmission dynamics of rabies in China. The model consists of susceptible, exposed, infectious, and recovered subpopulations of both dogs and humans and describes the spread of rabies among dogs and from infectious dogs to humans. The model simulations agree with the human rabies data reported by the Chinese Ministry of Health. We estimate that the basic reproduction number for the rabies transmission in China and predict that the number of the human rabies is decreasing but may reach another peak around 2030. We also perform some sensitivity analysis of in terms of the model parameters and compare the effects of culling and immunization of dogs. Our study demonstrates that (i) reducing dog birth rate and increasing dog immunization coverage rate are the most effective methods for controlling rabies in China; and (ii) large scale culling of susceptible dogs can be replaced by immunization of them.

Optimal risk management of human alveolar echinococcosis with vermifuge

In this study, we develop a bioeconomic model of human alveolar echinococcosis (HAE) and formulate the optimal strategies for managing the infection risks in humans by applying optimal control theory. The model has the following novel features: (i) the complex transmission cycle of HAE has been tractably incorporated into the framework of optimal control problems and (ii) the volume of vermifuge spreading to manage the risk is considered a control variable. With this model, we first obtain the stability conditions for the transmission dynamics under the condition of constant control. Second, we explicitly introduce a control variable of vermifuge spreading into the analysis by considering the associated control costs. In this optimal control problem, we have successfully derived a set of conditions for a bang-bang control and singular control, which are mainly characterized by the prevalence of infection in voles and foxes and the remaining time of control. The analytical results are demonstrated by numerical analysis and we discuss the effects of the parameter values on the optimal strategy and the transmission cycle. We find that when the prevalence of infection in foxes is low and the prevalence of infection in voles is sufficiently high, the optimal strategy is to expend no effort in vermifuge spreading.

A stochastic model of Echinococcus multilocularis transmission in Hokkaido, Japan, focusing on the infection process

Echinococcus multilocularis causes human alveolar echinococcus. In Japan, high prevalence of E. multilocularis among the fox population has been reported throughout Hokkaido. Accordingly, control measures, such as fox hunting and the distribution of bait containing Praziquantel, have been conducted. This study developed a transmission model for individuals in the fox population and included a stochastic infection process to assess the prevalence of E. multilocularis. To make our model realistic, we used the worm burden for each individual in the fox population. We assumed that the worm burden depends on the number of protoscoleces in a predated vole and the number of infection experiences. We carried out stochastic simulations with 1,000 trials for the situations of Koshimizu and Sapporo, Hokkaido, Japan. The distribution of the worm burden among foxes obtained using the model agreed with dissection data. The simulation indicates that a careful choice of season is necessary for an effective distribution of Praziquantel-containing bait. A stochastic model for E. multilocularis, which can assess the range of the prevalence in the fox population, would be helpful in analyzing their complex life-cycle and also in designing control strategies.

A model of Leptospirosis infection in an African rodent to determine risk to humans: seasonal fluctuations and the impact of rodent control

Human leptospirosis (Leptospira spp. infection) is a worldwide public health problem that is of greatest concern for humid tropical and subtropical regions. The magnitude of the problem in these areas is larger because of the climatic and environmental conditions the bacterium face outside their hosts but also because of the frequency of contacts between people and sources of infection. Rodents are thought to play the most important role in the transmission of human leptospirosis. We here model the dynamics of infection in an African rodent (Mastomys natalensis) that is thought to be the principal source of infection in parts of Tanzania. Our model, representing the climatic conditions in central Tanzania, suggests a strong seasonality in the force of infection on humans with a peak in the abundance of infectious mice between January and April in agricultural environments. In urban areas the dynamics are predicted to be more stable and the period of high numbers of infectious animals runs from February to July. Our results indicate that removal of animals by trapping rather than reducing the suitability of the environment for rodents will have the greater impact on reducing human cases of leptospirosis.

Implications of increased susceptibility to predation for managing the sylvatic cycle of Echinococcus multilocularis

The ability to increase the chances that infectious prey are taken by predators is an observed feature of many parasites that rely on one or more predator-prey relationships to complete their life-cycle. In the sylvatic life-cycle of Echinococcus multilocularis - the causative agent of human alveolar echinococcosis-- foxes are the final host, with voles acting as intermediate hosts. Here we review the evidence that E. multilocularis causes increased susceptibility to predation and present a general mathematical model for the sylvatic life-cycle. The ability to increase susceptibility to predation in the intermediate host reduces the sensitivity of the parasite population to adverse conditions. For example, there is no critical density of foxes below which the parasite is expected to die out, even if the effect of the parasite on infected prey is very small. We suggest that increased susceptibility to predation is a plausible explanation for the observed resilience of E. multilocularis during and following field trials of praziquantel baiting.

Mathematical modeling of Echinococcus multilocularis transmission

A mathematical model for the transmission cycle of Echinococcus multilocularis would be useful for estimating its prevalence, and the model simulation can be instrumental in designing various control strategies. This review focuses on the epidemiological factors in the E. multilocularis transmission cycle and the recent advances of mathematical models for E. multilocularis transmission.

Transmission dynamics of Echinococcus multilocularis; its reproduction number, persistence in an area of low rodent prevalence, and effectiveness of control

On the basis of high prevalences of Echinococcus multilocularis in the growing fox populations in Central Europe, its total biomass may have increased significantly in the past 20 years. E. multilocularis is now also found in areas outside the known endemic area in Central Europe. Therefore, E. multilocularis, the causative agent of a serious parasitic zoonosis, might be of major concern for public health and a challenge to control. Some experimental field trials to control E. multilocularis using an anti-worm drug reduced parasite burden in a contaminated region during the control campaign, but failed to eradicate the parasite completely. It was our aim to develop a mathematical model describing the biomass of egg, larval, and adult worm stages of the E. multilocularis life-cycle, and simulate a hypothetical control campaign. Additionally, we derived the reproduction number of this parasite and explored conditions for the persistence of the parasite's life-cycle. Our model shows that while control campaigns rapidly reduce the worm burden in the definitive host, and consequently eggs in the environment, the pool of larvae in the intermediate host remains large. The parasite's life-cycle persists in a region where prevalence in the intermediate host is low (∼1%). Therefore, we conclude that the parasite is likely to re-emerge if control is discontinued on the basis of reduced worm population. Continued treatment of the definitive host is required to eradicate the larval stage of the parasite from the intermediate host population.

Modeling the transmission of Echinococcus granulosus and Echinococcus multilocularis in dogs for a high endemic region of the Tibetan plateau

Echinococcus granulosus and Echinococcus multilocularis abundance and prevalence data, for domestic dogs of Shiqu County, Sichuan Province, People's Republic of China, were fitted to mathematical models to evaluate transmission parameters. Abundance models, assuming the presence and absence of immunity, were fit for both E. granulosus and E. multilocularis using Bayesian priors, maximum likelihood, and Monte Carlo sampling techniques. When the models were compared, using the likelihood ratio test for nested models, the model assuming the presence of immunity was the best fit for E. granulosus infection, with a purgation based prevalence of 8% (true prevalence interval of 8-19% based on the sensitivity of purgation) and a mean abundance of 80 parasites per dog, with an average infection pressure of 560 parasites per year. In contrast, the model assuming the absence of immunity was the best fit for E. multilocularis infection, with a purgation based prevalence of 12% (true prevalence interval of 13-33% based on the sensitivity of purgation) and a mean abundance of 131 parasites per dog, with an average infection pressure of 334 or 533 parasites per year assuming a 5 or 3 month parasite life expectancy, respectively. The prevalence data for both parasites was then fit to a set of differential equations modeling the transition between infection states in order to determine number of infectious insults per year. Infection pressure was 0.21, with a 95% credibility interval of 0.12 to 0.41, infections per year for E. granulosus and 0.52, with a 95% credibility interval of 0.29-0.77, infections per year for E. multilocularis assuming a 5 month parasite lifespan or 0.85, with a 95% credibility interval of 0.47-1.25 infections per year, assuming a 3 month E. multilocularis lifespan in dogs.

Interactions between landscape changes and host communities can regulate Echinococcus multilocularis transmission

An area close to the Qinghai-Tibet plateau region and subject to intensive deforestation contains a large focus of human alveolar echinococcosis while sporadic human cases occur in the Doubs region of eastern France. The current review analyses and compares epidemiological and ecological results obtained in both regions. Analysis of rodent species assemblages within quantified rural landscapes in central China and eastern France shows a significant association between host species for the pathogenic helminth Echinococcus multilocularis, with prevalences of human alveolar echinococcosis and with land area under shrubland or grassland. This suggests that at the regional scale landscape can affect human disease distribution through interaction with small mammal communities and their population dynamics. Lidicker's ROMPA hypothesis helps to explain this association and provides a novel explanation of how landscape changes may result in increased risk of a rodent-borne zoonotic disease.

Processes leading to a spatial aggregation of Echinococcus multilocularis in its natural intermediate host Microtus arvalis

The small fox tapeworm (Echinococcus multilocularis) shows a heterogeneous spatial distribution in the intermediate host (Microtus arvalis). To identify the ecological processes responsible for this heterogeneity, we developed a spatially explicit simulation model. The model combines individual-based (foxes, Vulpes vulpes) and grid-based (voles) techniques to simulate the infections in both intermediate and definite host. If host populations are homogeneously mixed, the model reproduces field data for parasite prevalence only for a limited number of parameter combinations. As ecological parameters inevitably vary to a certain degree, we discarded the homogeneous mixing model as insufficient to gain insight into the ecology of the fox tapeworm cycle. We analysed five different model scenarios, each focussing on an ecological process that might be responsible for the heterogeneous spatial distribution of E. mulitlocularis in the intermediate host. Field studies revealed that the prevalence ratio between intermediate and definite host remains stable over a wide range of ecological conditions. Thus, by varying the parameters in simulation experiments, we used the robustness of the agreement between field data and model output as quality criterion for the five scenarios. Only one of the five scenarios was found to reproduce the prevalence ratio over a sufficient range of parameter combinations. In the accentuated scenario most tapeworm eggs die due to bad environmental conditions before they cause infections in the intermediate host. This scenario is supported by the known sensitivity of tapeworm eggs to high temperatures and dry conditions. The identified process is likely to lead to a heterogeneous availability of infective eggs and thus to a clumped distribution of infected intermediate hosts. In conclusion, areas with humid conditions and low temperatures must be pointed out as high risk areas for human exposure to E. multilocularis eggs as well.

Echinococcosis

Echinococcosis is a near-cosmopolitan zoonosis caused by adult or larval stages of cestodes belonging to the genus Echinococcus (family Taeniidae). The two major species of medical and public health importance are Echinococcus granulosus and Echinococcus multilocularis, which cause cystic echinococcosis and alveolar echinococcosis, respectively. Both are serious and severe diseases, the latter especially so, with high fatality rates and poor prognosis if managed incorrectly. Several reports have shown that both diseases are of increasing public health concern and that both can be regarded as emerging or re-emerging diseases. In this review we discuss aspects of the biology, life cycle, aetiology, distribution, and transmission of the Echinococcus organisms, and the epidemiology, clinical features, treatment, and diagnosis of the diseases they cause. We also discuss the countermeasures available for the control and prevention of these diseases. E granulosus still has a wide geographical distribution, although effective control against cystic echinococcosis has been achieved in some regions. E multilocularis and alveolar echinococcosis are more problematic, since the primary transmission cycle is almost always sylvatic so that efficient and cost-effective methods for control are unavailable.

Echinococcus multilocularis: secondary poisoning of fox population during a vole outbreak reduces environmental contamination in a high endemicity area

This paper describes the role of fox population level on Echinococcus multilocularis infection in foxes in a highly endemic area in eastern France. Fox population level was monitored by spotlight survey at Le Souillot from 1989 to 2000, and from 1992 to 2000 at Chemin, a control site located in a low endemic area. The infection level of the fox population was estimated at Le Souillot from winter 1995 to winter 1999 using a coproantigen ELISA performed on faeces collected in the field. Population biomass of intermediate hosts (Microtus arvalis and Arvicola terrestris) was monitored using index methods from 1995 to 1999. At Le Souillot, a significant decline in the fox population level was recorded after spring 1997 (P<0.001), and the population level remained low until 2000. The decline occurred when 31% of the grassland area was treated with bromadiolone, an anticoagulant used at a large scale for the control of A. terrestris population outbreaks. No decline of population was recorded at Chemin, where bromadiolone was not used for rodent control. Significant differences among ELISA OD distributions in fox faeces were recorded for the five winters under study at Le Souillot (P=0.0004). The median of ELISA OD distribution was 0.209 and 0.207 before the population decline (winter 1995 and 1996, respectively), significantly increased to 0.306 just after the decline (winter 1997), and then significantly decreased to 0.099 and 0.104 afterwards (winter 1998 and 1999, respectively). Therefore, the decrease in infection level occurred during winter 1998, 1 year after the population decline, when the intermediate host biomass in the field was at its highest. These results suggest a complex dependence between the fox population level and E. multilocularis infection in a high endemicity area. Alternative ways to control fox population as a way to reduce E. multilocularis transmission in a given area are discussed.

Controlling Echinococcus multilocularis-ecological implications of field trials

Two field trials to reduce the prevalence of Echinococcus multilocularis in foxes have been conducted in recent years. Although both trials reduced prevalence considerably, they failed to eradicate the parasite in the study region. Following the control trial in northern Germany, prevalence recovered unexpectedly and rapidly, reaching pre-control levels five quarters (15 months) after the end of control. To understand the internal dynamics of the parasite-host system's reaction to control, we developed a spatially explicit simulation model, Echi. The simulation model incorporates the information available concerning fox tapeworm population dynamics. Using epidemiological parameters to adjust pre-control prevalence, the model predicts the temporal evolution of the prevalence of E. multilocularis in controlled foxes without departing from the range of uncertainty of the field data. However, the model does not predict the rapid pre-control recovery observed in the field trial. The deviation of the model's prediction from field data indicates the involvement of processes not yet taken into account. We modified the model step by step to mimic processes with the potential to cause the rapid post-control recovery of the prevalence of E. multilocularis in foxes. Neither the longevity of tapeworm eggs nor the migratory behaviour of foxes showed any influence on the post-control reaction of the parasite-host system. However, landscape structures leading to a heterogeneous distribution of infected foxes have the potential to alter the system's reaction to control. If infected foxes are concentrated in multiple clusters in the landscape, the model prediction tallied with the range of uncertainty of the field data. Such spatial distribution of infected foxes may be caused by differential abiotic conditions influencing the survival of tapeworm eggs. The model was found to comply best with field data if the foxes acquire partial immunity by being exposed to the fox tapeworm. Both hypotheses explaining the rapid post-control recovery of the prevalence of E. multilocularis observed in the fox population were supported by field data. Both hypotheses have far-reaching consequences for future control trials. The spatial aggregation of infected foxes would enable control efforts to be concentrated on these highly infected areas. However, the acquisition of immunity acts as a buffer to control, necessitating intensified control measures.

Improvement of a polymerase chain reaction assay for the detection of Echinococcus multilocularis DNA in faecal samples of foxes

A polymerase chain reaction (PCR) method was developed in order to permit a sensitive and specific identification of Echinococcus multilocularis DNA from fox faecal specimens. In an attempt to overcome problems related to the presence of endogenous PCR inhibitors in faecal extracts, we investigated a DNA extraction technique using an anion binding resin (Gene-Fizz). This simple and rapid procedure was applied to 61 faecal samples. Compared with the traditional microscopic examination, the sensitivity of PCR using Gene-Fizz was 82.3% and the specificity was 95.5%. No PCR signal was obtained for 20 Echinococcus granulosus isolates, showing that this method allowed discrimination between E. multilocularis and E. granulosus. Large-scale epidemiological surveys of fox excrements may be possible by using Gene-Fizz treatment prior to PCR amplification reactions.

A pocket guide to host-parasite models

Mathematical models have been used to describe the population dynamics of a wide range of host-parasite interactions. Mick Roberts here discusses mathematical models for the dynamics of helminth endoparasites of non-human mammalian hosts, paying particular attention to the density-dependent factors that regulate the parasite populations, and the interaction between parasite and wild or feral animal host populations.